What it means
A yield is the annual return an investor earns on a bond. The answer depends on how often interest is paid and reinvested, because earning interest twice a year yields slightly more than earning it once.
Markets therefore use conventions to state yields consistently. Under the semi-annual bond basis, the yield is the half-year return multiplied by two.
A bond that returns 3% every six months is quoted as 6%. This quoted figure is called a nominal annual rate because it does not include the benefit of compounding within the year.
The convention is also called the bond-equivalent yield in many markets. It allows investors to compare instruments that pay at different frequencies, such as a bond paying every six months and a note paying only at maturity, by converting both to a semi-annual basis.
Traders use it all the time when quoting prices for government and corporate bonds. To compare a semi-annual yield with a yield on another basis, you have to convert it.
The effective annual yield accounts for compounding and is slightly higher than the nominal quote. The gap becomes larger when the yield is higher.
For non-specialists, the main message is to check the basis before comparing yields. A bank deposit quoted on an annual basis and a bond quoted on a semi-annual basis are not strictly comparable without conversion.
A small difference of a few hundredths of a per cent may matter for big portfolios. Quotes can differ between markets and over time, so it is worth checking the pricing convention in any document.
A bond term sheet will normally state the yield basis and the day-count method, which is the rule for counting days when working out interest. Using the wrong convention can lead to small but real pricing errors.
In practice
Real-world examples.
Example
A bond trader sees two quotes: one bond at 5.5% on a semi-annual bond basis and a deposit at 5.6% on an annual basis. She converts the bond to an effective annual yield of about 5.58% before comparing. This shows the two are almost identical.
Example
A treasury analyst values a government bond paying a 4% coupon twice a year. He quotes its yield on a semi-annual bond basis for use in a pricing system. The system then converts it to other bases when needed, such as an annual or quarterly basis, so that every report uses the same measure.
Example
A corporate finance team compares a bond offering at 7% semi-annual with a loan costing 7.1% annually. They convert the 7% to an effective annual rate of 7.12% and conclude the loan is slightly cheaper. The difference is small but matters on a large debt.
Formula
Calculation
Effective annual yield = (1 + SABB yield / 2)^2 - 1
A bond is quoted at 6% on a semi-annual bond basis. The half-year rate is 6% / 2 = 3%, so each $1,000 of bond earns $30 every six months. The effective annual yield is (1 + 0.03)^2 - 1 = 1.0609 - 1 = 0.0609, which is 6.09%. In dollar terms, a $1,000 investment grows by $60.90 over a year if the first $30 coupon is reinvested at 3%.Case study
Seen in the real world.
Oakmont Utilities is a fictional company evaluating two ways to raise $20,000,000. One option is a bond quoted at 6.2% on a semi-annual bond basis, and the other is a bank loan at 6.3% with annual compounding.
The treasurer, Beatrice, converted the bond to an effective annual rate of (1 + 0.031)^2 - 1 = 6.30%, which was essentially the same as the loan. This is an illustrative story, but it illustrates why the quoting basis matters. At first glance the bond looked cheaper by 0.1 percentage points, yet once the same basis was used the costs were equal, so she chose by flexibility and fees instead.
Beatrice added a conversion line to the company's standard financing comparison template. Future decisions would then compare all options on the same effective annual basis.
Watch out
Common mistakes.
- Comparing a semi-annual yield directly with an annual yield. The two use different compounding assumptions and should be converted first.
- Treating the quoted yield as the true annual return. The effective annual yield is slightly higher because of the extra compounding.
- Assuming all bonds pay twice a year. Some pay annually or quarterly, so check the coupon frequency before using the convention.
Questions
People also ask.
What does semi-annual bond basis mean?
It is a convention that quotes an annual yield by doubling the six-month yield.
Is it the same as bond-equivalent yield?
In many markets the two terms are used for the same convention, although some usage differs slightly, so check the definition in your market.
How do I convert it to an effective annual yield?
Divide the quoted yield by two, add one, square the result and subtract one.
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